Those are definitely seedlings of some sort of Oak (Quercus sp.), not related to any Rhus sp. from which you'd get a rash.

It appears that the persistent marcescent leaves have bristle tips on the lobes, pointing to affinity with the Red Oak group of oaks - rather than the White Oak group which lack bristle tips on leaf lobes.

There are many species of oaks in the Red Oak group native to coastal and Piedmont North Carolina (you even live near Red Oak, NC).

To choose a tree of any sort, not just an oak ask yourself a few questions:

How tall will it ultimately grow: Are there overhead power lines? Will it block a nice view?
Which way does the shadow fall? Is shade in that area OK?
How wide will it ultimately grow: The trunk needs room to grow a large diameter, the roots need room to spread, and the canopy will spread. If it overhangs the house there is the threat of a limb breaking and falling on the house. If the trunk and roots are too close to pavement or building they will ultimately grow into that structure or lift the pavement.

Is the leaf fall OK? Will you clean it up? Let it lie? Turn it into compost?

Most lawns require something close to full sun so a lawn is impossible under a wide spreading, dense tree unless you can prune it (or have it professionally pruned) to keep it thin enough.

If your space cannot handle a large tree, then assess just what size tree will work, and research the trees that stay within that acceptable size range. Do not get a too-big tree saying 'Well, I can prune it'.

Specifically about Oaks:
Even the smallest, I would keep at least 10' away from house and pavement, and 20' is better for most smaller species (Oaks are not really small). Even farther for the largest ones. Many are not trees for a small yard at all.

Many Oaks are OK in a lawn, usually in an area that is cut out as a planter area, but can be surrounded by lawn. Not lawn right up to the trunk. Just make sure you are not watering the lawn too frequently (which is bad for the lawn, anyway). But remember that as they grow the oak will increasingly shade the lawn.